Quantales of open groupoids

SGF-Quantales and their groupoids

Étale groupoids and their quantales

We establish a close and previously unknown relation between quantales and groupoids, in terms of which the notion of étale groupoid is subsumed in a natural way by that of quantale. In particular, to each étale groupoid, either localic or topological, there is associated a unital involutive quantale. We obtain a bijective correspondence between localic étale groupoids and their quantales, whic...

Quantales as geometric objects: symmetry beyond groupoids?

Modern mathematics has become pervaded by the idea that in order to cater for certain notions of symmetry, in particular of a local nature, one needs to go beyond group theory, replacing groups by groupoids. A nice survey of some implications of this idea in algebra, geometry, and analysis (as of 1996) can be found in [19]. The same idea can be expressed in terms of pseudogroups, which provide ...

Lectures on étale groupoids, inverse semigroups and quantales

complete pseudogroups L∨ bb

Actions of vector groupoids

In this work we deal with actions of vector groupoid which is a new concept in the literature‎. ‎After we give the definition of the action of a vector groupoid on a vector space‎, ‎we obtain some results related to actions of vector groupoids‎. ‎We also apply some characterizations of the category and groupoid theory to vector groupoids‎. ‎As the second part of the work‎, ‎we define the notion...